Optimal. Leaf size=73 \[ -\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125} \]
[Out]
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Rubi [A] time = 0.0902944, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{324 x^{6}}{125} - \frac{324 x^{5}}{3125} + \frac{22977 x^{4}}{6250} - \frac{393 x^{3}}{625} + \frac{109032 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{424432}{390625}\, dx - \frac{62097 \int x\, dx}{15625} - \frac{19239}{1953125 \left (5 x + 3\right )} - \frac{1331}{3906250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**5/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0583319, size = 68, normalized size = 0.93 \[ \frac{-1265625000 x^8-1569375000 x^7+1278703125 x^6+1828837500 x^5-692475000 x^4-744310000 x^3+711123525 x^2+698557830 x+1090320 (5 x+3)^2 \log (6 (5 x+3))+151973789}{19531250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^5)/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.01, size = 56, normalized size = 0.8 \[{\frac{424432\,x}{390625}}-{\frac{62097\,{x}^{2}}{31250}}-{\frac{393\,{x}^{3}}{625}}+{\frac{22977\,{x}^{4}}{6250}}-{\frac{324\,{x}^{5}}{3125}}-{\frac{324\,{x}^{6}}{125}}-{\frac{1331}{3906250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{19239}{5859375+9765625\,x}}+{\frac{109032\,\ln \left ( 3+5\,x \right ) }{1953125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^5/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.3289, size = 76, normalized size = 1.04 \[ -\frac{324}{125} \, x^{6} - \frac{324}{3125} \, x^{5} + \frac{22977}{6250} \, x^{4} - \frac{393}{625} \, x^{3} - \frac{62097}{31250} \, x^{2} + \frac{424432}{390625} \, x - \frac{121 \,{\left (318 \, x + 193\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{109032}{1953125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^5*(2*x - 1)^3/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211732, size = 97, normalized size = 1.33 \[ -\frac{253125000 \, x^{8} + 313875000 \, x^{7} - 255740625 \, x^{6} - 365767500 \, x^{5} + 138495000 \, x^{4} + 148862000 \, x^{3} - 57470475 \, x^{2} - 218064 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 38006490 \, x + 116765}{3906250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^5*(2*x - 1)^3/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.313781, size = 63, normalized size = 0.86 \[ - \frac{324 x^{6}}{125} - \frac{324 x^{5}}{3125} + \frac{22977 x^{4}}{6250} - \frac{393 x^{3}}{625} - \frac{62097 x^{2}}{31250} + \frac{424432 x}{390625} - \frac{38478 x + 23353}{19531250 x^{2} + 23437500 x + 7031250} + \frac{109032 \log{\left (5 x + 3 \right )}}{1953125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**5/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.209003, size = 70, normalized size = 0.96 \[ -\frac{324}{125} \, x^{6} - \frac{324}{3125} \, x^{5} + \frac{22977}{6250} \, x^{4} - \frac{393}{625} \, x^{3} - \frac{62097}{31250} \, x^{2} + \frac{424432}{390625} \, x - \frac{121 \,{\left (318 \, x + 193\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{109032}{1953125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^5*(2*x - 1)^3/(5*x + 3)^3,x, algorithm="giac")
[Out]